Solve.Draw a rectangular fraction model to explain yourthinking.Then, write a number sentence.1/3of3/7=

The correct statement is-number of students in the data set

In research and data collecting, something that is being measured and whose values can change is referred to as a variable.

Given that we have a range of alternatives from January to December, the aforementioned example demonstrates how the student birth month is a variable. The student's ability to indicate whether they support particular political parties or not makes their political affiliation another variable. Since they are college students, the age of the student is another variable, with replies falling within a range of 20 to 25.

Since students will give different answers, whether they live at the same address or a different one, student address is also a variable.

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a) Option a) 9 - 1/2 is equal to 17/2.

b) Option b) 27 - 2/3 is equal to 79/3.

a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.

Multiplying 9 by 2/2, we get:

9 * (2/2) = 18/2

So, the expression 9 - 1/2 can be simplified to:

18/2 - 1/2 = 17/2

Therefore, option a) 9 - 1/2 is equal to 17/2.

b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.

Multiplying 27 by 3/3, we get:

27 * (3/3) = 81/3

So, the expression 27 - 2/3 can be simplified to:

81/3 - 2/3 = 79/3

Therefore, option b) 27 - 2/3 is equal to 79/3.

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Answer:

Step-by-step explanation:

\(d^2=(x_2-x_1)^2+(y_2-y_1)^2\\ \\ d^2=(-7+7)^2+(5+4)^2\\ \\ d^2=81\\ \\ d=9\)

9514 1404 393

Answer:

  5.  4√2 N

  6. 20 N

Step-by-step explanation:

We're not sure how your diagram relates to the notion of the weight being "pushed". Usually T represents "tension," which would indicate a "pull" in up and to the right.

__

5. The side ratios in this triangle match exactly those in your problem 1. T is √2 times the equal side lengths, so is T = 4√2 N.

__

6. The sides ratios in the triangle match exactly those in your problem 2. T is 2 times the shorter side length, so is T = 20 N.

Answer:

A: A^-1 = [[-2,-3,-1.5],[-2,-4,-2.5],[-1,1,-.5]]

Step-by-step explanation:

Answer:

To find the inverse of the matrix A, we will use the row reduction method. We will augment matrix A with the identity matrix I and perform row operations until A is transformed into the identity matrix. The resulting matrix on the right side will be the inverse of A.

Step-by-step explanation:

Augment the matrix A with the identity matrix I:

[ 1  0 -3 | 1  0  0 ]

[ 3  1 -4 | 0  1  0 ]

[ 4  2 -4 | 0  0  1 ]

Perform row operations to transform the left side of the augmented matrix into the identity matrix:

R2 = R2 - 3R1

R3 = R3 - 4R1

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  2  8 | -4  0  1 ]

Perform row operations to further transform the left side of the augmented matrix into the identity matrix:

R3 = R3 - 2R2

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  0 -2 | 2  -2  1 ]

Multiply the third row by -1/2 to make the pivot element of the third row equal to 1:

R3 = (-1/2) * R3

[ 1  0 -3 | 1  0  0 ]

[ 0  1  5 | -3  1  0 ]

[ 0  0  1 | -1  1  -1/2 ]

Perform row operations to further transform the left side of the augmented matrix into the identity matrix:

R1 = R1 + 3R3

R2 = R2 - 5R3

[ 1  0  0 | 2  0  3/2 ]

[ 0  1  0 | 2  -4  5/2 ]

[ 0  0  1 | -1  1  -1/2 ]

The resulting matrix on the right side of the augmented matrix is the inverse of matrix A:

[ 2  0  3/2 ]

[ 2  -4  5/2 ]

[ -1  1  -1/2 ]

Therefore, the inverse of matrix A is:

[ 2  0  3/2 ]

[ 2  -4  5/2 ]

[ -1  1  -1/2 ]

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

(B)A': (p, m) and B': (z, −w)

Step-by-step explanation:

Line AB has a negative slope and goes through points (-m, p) and (w, z).

Line A'B' has a positive slope and intersects with line AB.

Definition: Two lines are perpendicular if the product of their slopes is -1.

Slope of AB

\(m_1=\dfrac{z-p}{w-(-m)} \\m_1=\dfrac{z-p}{w+m}\)

From the options, we consider the coordinates whole slope multiplied by the slope of AB gives a result of -1.

In Option B: A': (p, m) and B': (z, −w)

Slope of A'B'

\(m_2=\dfrac{-w-m}{z-p} \\m_2=\dfrac{-(w+m)}{z-p}\)

The product of the slopes

\(m_1m_2=\dfrac{z-p}{w+m}\times \dfrac{-(w+m)}{z-p} =-1\)

Therefore, the coordinate for points A' and B' which would help prove that lines AB and A'B' are perpendicular is A': (p, m) and B': (z, −w).

You can try to calculate the slope of the others. They would not satisfy this condition.

Answer:

B. A': (p, m) and B': (z, −w)

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

The quantity of sheep and goats are in a ratio of 6 to 8.

Suppose there are 6x - sheep, 8x- goats

8x=48

x=6

6*6=36- the amount of sheep

48+36=84

Answer:

×=3

Step-by-step explanation:

6x-4 = x+11

6x-x = 11+4

5x = 15

x = 3

Answer:

80miles/hr

0.9hr

Step-by-step explanation:

Given parameters:

Distance traveled  = 60miles

Time taken = 0.75hrs

Unknown:

Speed of the car = ?

Time it will take to cover 72miles  = ?

Solution:

Speed is the distance divided by time;

   Speed  = \(\frac{distance}{time}\)

  Insert the parameters and solve;

     Speed  = \(\frac{60}{0.75}\)  = 80miles/hr

Time taken;

   Time  = \(\frac{distance}{speed}\)  = \(\frac{72}{80}\)   = 0.9hr

Answer:

$25.20

Step-by-step explanation:

($5.40) / ($0.30/day) = 18 days

It took 18 days for Gill to save $5.40 more than Devi.  So in those 18 days Devi saved:

$1.40/day x 18 days = $25.20

The greatest common factor of 3t²-6t+3 is 3, so the equation can be factored as 3(t²-2t+1).

Factor is a mathematical term used to describe a number that divides into another number exactly. It is a number that can be multiplied by other numbers to produce a given product. Factors are used in a wide variety of mathematical applications, including solving equations and finding prime numbers. Factors can also be used to calculate fractions, and to determine the greatest common factor (GCF) of a set of numbers.

This is done by dividing each term by the common factor and rearranging the terms to look for a pattern. By doing this, the equation can be further simplified.

Factoring out the greatest common factor is useful in many mathematical operations, such as solving equations and finding the roots of polynomials. It can help reduce the complexity of an equation and provide insight into the behavior of the equation. By factoring out the greatest common factor, we can see that the original equation can be broken down into two simpler terms, 3 and (t²-2t+1), which can be further simplified. This can make it easier to solve the equation or find its roots.

Factoring out the greatest common factor can also help determine the nature of the equation. If the original equation 3t²-6t+3 had a common factor of 3, then it is clear that the equation is a polynomial with degree two. In contrast, if the greatest common factor had been 1, then the equation would have been a linear equation.

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The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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The changes in account balances for Elder Company for 2021 are net income will be $160000

We have given debt common stock = $680000

Credit liabilities = 350000

Credit paid in capital = 190000

And an excess of par 30,000 credit Assuming the only changes in retained earnings

So 680000 = 350000+190000+30000+ retained earning

Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.

So retained earning = $110000

Dividend paid = $50000

So Net income = dividend paid + retained earning

Net income = $110000+$50000

Net income = $160000

So option (c) will be the correct answer.

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For given functions, The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

What is the definition of a function?

A function is a mathematical rule that gives each input value a distinct output value. A function is officially defined as a collection of ordered pairs (x, y) in which each input value x is coupled with exactly one output value y. The domain of the function refers to the input values, while the range refers to the output values. A graph, table, equation, or verbal explanation can all be used to depict a function. When the input value is x, the notation f(x) is commonly used to express the output value of a function f.

Now,

From given function f(x) and g(x)

For f(x) when x=0 then y=1 or y-intercept=1

for g(x), the y-intercept is 1 from equation y=4x+1

and slope of g(x)=4

and slope of f(x)=(11-1)/(2-0)

=10/5

=2

Hence,

           The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

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If FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

The ∠ACD is a straight angles

We know the angles on a straight line add up to 180 degree

Therefore,

The measure of angle ACD = 180 degrees

Here it is given that the line FC bisects angle ACD

Therefore, The angle ACF is equal to Angel DCF

Angle ACF = Angel DCF

Angle ACF + Angle DCF = 180 degrees

Then,

Angle ACF = Angel DCF  = 90 degrees

Hence, if FC bisects ∠ACD and ∠ACD is a straight angles, then proved that the ∠ACF is a right angle

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Estimated volume of the tree as per given height and circumference using trapezoidal rule is equal to 30907.5 cubic inches.

As given in the question,

Given height 'x' and circumference 'y=f(x)',

Height (inches)  'x'            :       0    15     30    45      60      75      90

Circumference (inches) 'y=f(x)':      31   28    21    17      12      8        2

Trapezoidal rule :

Δx = (b - a ) n

Here b = 90

a = 0

n =6

Δx = ( 90 - 0)/6

    = 15

Substitute the value to get the volume using trapezoidal rule:

T₆=(Δx/2)[f(x₀)²+ 2{f(x₁)²+ f(x₂)²+f(x₃)² + f(x₄)²+f(x₅)²}+ f(x₅)²]

   = (15/2)[ 31² + 2 (28² + 21² + 17² + 8²) + 2² ]

   = ( 15/2) [961 + 2{ 784+ 441 + 289 + 64} + 4]

   = 15 × 2060.5

   =   30907.5 cubic inches

Therefore, the volume of the tree as per given given table using trapezoidal rule is equal to 30907.5 cubic inches.

The above question is incomplete , the complete question is:

The circumference of a tree at different heights above the ground is given in the table below. Assume that all horizontal cross-sections of the tree are circles. Estimate the volume of the tree using the trapezoid rule. There needs to be six subdivisions in the trapezoid rule.

Height (inches) :                  0    15     30    45      60      75      90

Circumference (inches):      31   28    21    17      12      8        2

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According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.

To illustrate this value on an abacus we must find the number of this operation as shown below:

Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:

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The cement and gravel must be used in construction is 60 and 80.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or \(\dfrac{a}{b}\)

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

\(a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3\)

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Given that;

Ratio of cement:sand:gravel= 1:2.5:3.7

The weight of sand bag 150lb.

Let & be the proportion of cement in a mixture. The ratio of cement to sand is given as 1 : 2.5. With a 150-lb sand, then the proportion of cement is given by

1/2.5 = x/150

150=2.5x

x=150/2.5

x=1500/25

x=60

y= 80

Therefore, by the given ratio answer will be 60 and 80.

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The correct statement regarding the function g(x), considering it's domain and range, is given as follows:

D. g(3) = 18.

Before knowing the definition of the domain and the range of a function, the input and the output of a function must be identified. In this function, they are given as follows:

The domain of a function is composed by all the values assumed by the input of the function. Hence, in this problem, g(x) can only be calculated for values of x that are between -1 and 4, inclusive. g(-5) and g(5), for example, cannot be calculated.

The range of a function is composed by all the values assumed by the output of the function. Hence, in this problem, the values assumed by g(x) must be between 0 and 18, inclusive, thus values such as g(x) = -1 or g(x) = 19 are not valid.

Thus the correct statement is given as follows:

As:

The options are given as follows:

A. g(5) = 12.

B. g(1) = -2.

C. g(2) = 4.

D. g(3) = 8.

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Answer:

I can't really see it so i don't know I'm sorry

Answer:

15

Step-by-step explanation:

Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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The table has been filled with the correct values

He uses 2 cups of sugar for every 3 cups of lemon juice

Number of cups of sugar is proportional to the number of cups of lemon juice

Number of cups of sugar = x

Number of cups of lemon juice = y

y ∝ x

y = kx

k = y/x

= 3 / 2

= 1.5

Then

Number of cups of sugar for 9 cups of lemon juice = 9/ 1.5

= 6 cups

Number of cups of lemon juice when 10 cups of sugar = 10 × 1.5

= 15 cups

Number of cups of lemon juice when 12 cups of sugar = 12 × 1.5

= 18 cups

Hence, the table has been filled with the correct values

The complete question is:

Abdul loves to make fresh lemonade in the summer. In his recipe, he uses 2 cups of sugar for every 3 cups of lemon juice. Fill the table

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Indefinite integral using integration by parts from x2 ln(x) dx is

\(\frac{1}{3}\) \(X^{3\\}\) (ln(x) - \(\frac{1}{3}\)) + C

The given choice of u and dv

∫ \(x^{2} ln(x) dx\)

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  \(ln(x)\)     du = \(\frac{1}{x}\)\(dx\)

dv = \(x^{2}\)         v = \(\frac{1}{3}x^{3}\)

∫ u dv = uv - ∫ v du

∫ \(x^{2} ln(x) dx\)   =  ln(x) \(\frac{1}{3}x^{3}\) - ∫ \(\frac{1}{3}x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3} . x^{-1}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{2}\) dx     ----> ∫ \(x^{2}\) dx = \(\frac{1}{3} x^{3} + C\)

                    =  \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) \(\frac{1}{3} x^{3} + C\)

                    = \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

Therefore Indefinite integral using integration by parts

∫ \(x^{2} ln(x) dx\)  is  \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

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The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Answer:

3.4 lessons per week

Step-by-step explanation:

If the teacher has to teach 6 chapter in 15 weeks, and each chapter has around 8.5 lessons. it means that the teacher has to teach in 15 weeks a total amount of lessons of 6*8.5= 51.

so 15 weeks---51 lessons

    1 week------x

From the above relation we have= 51/15= 3,4 lessons per week

1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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